To form $x_n$: any valid sequence of $n-1$ days, followed by a non-all-1s day. There are $127$ such (since $128 - 1 = 127$), and for each, $127$ choices: - Treasure Valley Movers

Why More US Users Are Exploring How to Form Real, Sustainable Daily Streaks—And What It Really Means

Ever notice how people are quietly fixing small, consistent habits—only to stop when they hit “all-1s”? There’s a subtle pattern behind this: forming a sequence of consecutive days with one non-repetitive break. Specifically, take any 4-day block where the first 3 are the same, followed by one day that isn’t all the same. There are exactly 127 of these (since there are 128 total daily states, minus the $1–1$ repetition), and